Electron. J. Differential Equations, Vol. 2024 (2024), No. 63, pp. 1-17.

Curved-pipe flow with boundary conditions involving Bernoulli pressure

Tvrtko Doresic, Igor Pazanin

Abstract:
In this article, we study the steady-state flow of the incompressible viscous fluid through a thin distorted pipe with an arbitrary central curve. We prescribe the inflow and outflow boundary conditions involving the Bernoulli pressure with a given pressure drop. Using the multiscale expansion technique with respect to the pipe's thickness, we construct the higher-order asymptotic approximation of the flow given by the explicit formulae for the velocity and pressure. We also perform a detailed error analysis justifying the usage of the proposed solution and indicating its order of accuracy.

Submitted May 15, 2024. Published October 22, 2024.
Math Subject Classifications: 35C20, 35Q35, 76M45.
Key Words: Newtonian fluid; Bernoulli pressure boundary condition; curved pipe; asymptotic analysis
DOI: 10.58997/ejde.2024.63

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Tvrtko Doresic
Department of Mathematics
Faculty of Science
University of Zagreb
Croatia
email: tvrtko.doresic@math.hr
Igor Pazanin
Department of Mathematics
Faculty of Science
University of Zagreb
Croatia
email: pazanin@math.hr

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